Photovoltaic System Having Power-Increment-Aided Incremental-Conductance Maximum Power Point Tracking Controller Using Variable-Frequency and Constant-Duty Control and Method Thereof

ABSTRACT

The configurations of photovoltaic system and methods thereof are provided. The proposed photovoltaic system includes a PI-INC MPPT controller using a variable-frequency constant-duty (VFCD) control and guided by an Ipv-Vpv curve and a Ppv-Vpv curve.

CROSS-REFERENCES TO RELATED APPLICATIONS

The application claims the benefit of Taiwan Patent Application No.101109928, filed on Mar. 22, 2012, in the Taiwan Intellectual PropertyOffice, the disclosures of which are incorporated herein in theirentirety by reference.

FIELD OF THE INVENTION

The present invention relates to a photovoltaic (PV) system having apower-increment-aided incremental-conductance (PI-INC) maximum powerpoint tracking (MPPT) controller. In particular, it relates to thephotovoltaic system having the PI-INC MPPT controller using avariable-frequency constant-duty control.

BACKGROUND OF THE INVENTION

FIG. 1( a) shows a circuit diagram of an equivalent circuit of a typicalsolar cell unit, wherein D is an LED, Rsh is a parallel-connected innerresistor, Rs is a series-connected inner resistor, and Iph is an outputcurrent of the solar cell unit. There are six well-known solar energyMPPT techniques including voltage feedback method, power feedbackmethod, practical measurement method, linear approximation method,perturbation and observation method and incremental conductance method.

In these six methods, the perturbation and observation method is themost widely used one. This method uses the perturbation to measure thenew output voltage and current of the two sides of the solar panel,calculate its power, and compare with the power sampled last time to getits change amount. If the new power value is higher than the power valueof last time, it represents that the perturbation direction is correct.Otherwise, the direction of perturbation shall be reversed. And, thenext movement of adding or subtracting the perturbation is decidedaccordingly. Since the procedure of perturbation will constantly changethe output power of the solar panel (or the PV array), the lastoperating point would be stabilized within a small range around themaximum power point (MPP). The drawback of this method is that theprocedure of perturbation will never be ceased, which will causeoscillation around the MPP, result in the energy loss and decrease theefficiency of conversion.

The incremental conductance method is applied via a principle that arate of change of an output power with respect to a voltage of a solarpanel is zero at an MPPT, and at a place corresponding to dP/dV=0 on thecurrent-voltage characteristic curve, e.g. as shown in FIG. 1( b), andthe incremental conductance method directly finds out

$\begin{matrix}{{\frac{\Delta \; I}{\Delta \; V} = {- \frac{I}{V}}},} & (1)\end{matrix}$

where I is a solar cell current, V is a solar cell voltage, ΔV is avoltage increment, and ΔI is a current increment. Via measuring aconductance value of ΔI/ΔV and compared it with an instantaneousconductance of −I/V of the solar panel to judge whether ΔI/ΔV is largerthan, smaller than, or equivalent to −I/V so as to determine whether thenext incremental change should be continued. When the incrementalconductance conforms to formula (1), the solar panel is for sure to beoperated at a maximum power point (MPP), and there will be no more nextincrement. This method engages in a tracking via the modification of thelogic expression, there is not any oscillation around the MPP such thatit is more suitable to the constantly changing conditions of theatmosphere. The incremental conductance method can accomplish the MPPTmore accurately and decrease the oscillation problem as in theperturbation and observation method, but it still has some drawbacks. Asshown in FIG. 1( b), using the curve of insolation 1000 W/m2 as anexample, if it is detected at the very beginning that the solar panel isworking at point A on the Ipv-Vpv curve, that is at the left-hand sideof point C (the MPP), and corresponding to point A′ on the Ppv-Vpvcurve, the (photovoltaic) system will cause the solar panel to move itsoperating point from A to its right-hand side and track towards thepoint C. On the contrary, if it is detected that the solar panel isworking at point B on the Ipv-Vpv curve, that is at the right-hand sideof point C (the MPP), and corresponding to point B′ on the Ppv-Vpvcurve, then the system will cause the solar panel to move its operatingpoint from B to its left-hand side and track towards the point C.Finally, when the detected conductance value of ΔI/ΔV satisfies formula(1), the system will keep the operating point of the solar panel atpoint C of the Ipv-Vpv curve and at point C′ of the Ppv-Vpv curve tomaintain the maximum power output of the solar panel. However, thedrawbacks of the incremental conductance method are that at theleft-hand side of point C (the MPP) of the Ipv-Vpv curve, it is foundthat the change of current with respect to voltage is almost a constantvalue in most of the sections, and is approximately equal to theshort-circuit current, and at the right-hand side of point C, theproblem is the change of voltage with respect to current is not obvious.In other words, at the left-hand side of point C, the change of currentwith respect to voltage is relatively insensitive and has a poorresponsibility. On the contrary, at the right-hand side of point C, thechange of voltage with respect to current is relatively insensitive.However, the best tracking range of the incremental conductance methodis in the area around point C, where the changes of current and voltageare relatively obvious, and it has a superior responsibility. But, onthe left-hand side and the right-hand side of point C, there arerespectively drawbacks of the change of current with respect to voltageis relatively insensitive and the change of voltage with respect tocurrent is relatively insensitive such that result in the incrementalconductance method could not give full scope of its function and thereare phenomena of tardiness and slow response speed when engaged in theMPPT, which will influence the output efficiency of the maximum power.

Keeping the drawbacks of the prior arts in mind, and employingexperiments and research full-heartily and persistently, the applicantfinally conceived a photovoltaic system having a power-increment-aidedincremental-conductance maximum power point tracking controller using avariable-frequency constant-duty control and method thereof.

SUMMARY OF THE INVENTION

It is a primary objective of the present invention to provide aphotovoltaic system having a power-increment-aidedincremental-conductance maximum power point tracking controller using avariable-frequency constant-duty control. This technique includesPI-MPPT and INC-MPPT, and sets up a threshold tracking zone in the areawith obvious changes on the Ipv-Vpv curve around point C. If the powerincrement falls into the threshold tracking zone, the system enters theINC fine tracking and uses the Ipv-Vpv curve as a tracking standard. Onthe contrary, if the power increment falls outside the thresholdtracking zone, the system enters the PI coarse tracking and uses thePpv-Vpv curve as a tracking standard. The proposed photovoltaic systemhas a relatively quick response and a relatively better outputefficiency of the maximum power when engaged in the MPPT.

According to the first aspect of the present invention, a photovoltaicsystem with a photovoltaic current (Ipv), a photovoltaic voltage (Vpv),a photovoltaic power (Ppv), a control frequency (fs) and an output power(Po), wherein there is a derivative (dIpv/dVpv) of Ipv with respect toVpv includes a power-increment-aided incremental-conductance (PI-INC)maximum power point tracking (MPPT) controller guided by a controlchart, wherein the control chart includes an Ipv-Vpv curve and a Ppv-Vpvcurve, a dIpv/dVpv-Vpv curve, a dIpv/dVpv-fs curve, and a Po-fs curve.

According to the second aspect of the present invention, a photovoltaicsystem with a photovoltaic current (Ipv), a photovoltaic voltage (Vpv)and a photovoltaic power (Ppv) includes a controller having circuitcharacteristics represented by an Ipv-Vpv curve and a Ppv-Vpv curve.

According to the third aspect of the present invention, a method foroperating a controller of a photovoltaic system with a photovoltaiccurrent (Ipv), a photovoltaic voltage (Vpv) and a photovoltaic power(Ppv), includes a step of: providing an Ipv-Vpv curve and a Ppv-Vpvcurve to be used to determine whether a specific conductance derivativeratio of dIpv/dVpv enters a threshold tracking zone.

The present invention can be best understood through the followingdescriptions with reference to the accompanying drawings, in which:

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1( a) shows a circuit diagram of an equivalent circuit of a typicalsolar cell unit;

FIG. 1( b) shows a waveform diagram with Ipv-Vpv and Ppv-Vpv curveshaving designated threshold tracking zones;

FIGS. 2( a)-2(b) respectively show the a waveform diagram of the varioustracking routes of the PI-INC MPPT method proposed by the presentinvention and the INC MPPT method when they are fallen on the right-handside and the left-hand side of the MPP;

FIG. 3( a) shows a circuit diagram of a photovoltaic charger accordingto the preferred embodiment of the present invention;

FIG. 3( b) shows a waveform diagram of predicted dynamic states withinsolation change of the photovoltaic charger as shown in FIG. 3( a);

FIG. 3( c) shows an equivalent circuit diagram of the control-to-outputmodel drawing energy from the PV array of the photovoltaic charger asshown in FIG. 3( a);

FIG. 4 shows a waveform diagram of control chart of the controller ofthe photovoltaic charger according to the preferred embodiment of thepresent invention;

FIG. 5( a) shows a flow chart of main program of an algorithm of PI-INCMPPT using VFCD according to the preferred embodiment of the presentinvention;

FIG. 5( b) shows a flow chart of subroutine of an algorithm of PI-INCMPPT using VFCD according to the preferred embodiment of the presentinvention;

FIGS. 6( a)-(b) respectively show a waveform diagram of output currentversus switching frequency and output power versus switching frequencyunder various solar insolations of the proposed photovoltaic chargerusing VFCD;

FIGS. 7( a)-(b) respectively show the interleaved high frequency tinypulse currents (ip1, ip2) and the interleaved secondary side currents(is1, is2) under the sun insolation of 1 Kw/m²; and

FIG. 8 shows waveform diagram comparing PI-INC MPPT and INC-MPPT interms of dynamic tracking behavior for various insolation changes.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Although the following description contains many specifications for thepurposes of illustration, anyone of ordinary skill in the art willappreciate that many variations and alterations to the following detailsare within the scope of the invention. Accordingly, the followingpreferred embodiment of the invention is set forth without any loss ofgenerality to and without imposing limitations upon, the claimedinvention.

Due to the aforementioned drawbacks of the prior art, the presentinvention provides a PI-INC MPPT technique, this technique consists ofPI-MPPT and INC-MPPT, the PI-MPPT is named as coarse-tracking and theINC-MPPT is named as fine-tracking. This motivation results from theobservation of the power curve Ppv-Vpv as shown in FIG. 1( b). At thetwo sides of the MPP C′, the changes of the power are in directproportion to the voltage, and there is no such problems of tardinessand insensitive response area as those on the Ipv-Vpv curve. Thus, theproposed method of the present invention preserves the unique advantageof accurately tracking around the MPP C of the incremental conductancemethod, that is to set up the threshold tracking zone (TTZ) in the areahaving obvious changes on the Ipv-Vpv curve around point C as shown inFIG. 1( b), which is equivalent to define the points (ρ1, ρ2) on theIpv-Vpv curve as a conductance threshold zone (CTZ=ΔC), or correspondingto define points (P_(ρ1), P_(ρ2)) on the Ppv-Vpv curve as a powerthreshold zone (PTZ=ΔP). The principles of this technique are that thesystem detects the power P_(n+1) generated by the new output voltage andthe new output current of the two sides of the solar panel, and P_(n+1)is compared with the previously sampled power Pn, that is the powerincrement ΔP=P_(n+1)−P_(n). If the power increment ΔP falls into therange of threshold (P_(ρ1), P_(ρ2)), the system will immediately enterthe fine-tracking of the incremental conductance, and use the Ipv-Vpvcurve as the tracking standard. On the contrary, if the power incrementΔP falls outside the range of threshold (P_(ρ1), P_(ρ2)), the systemwill immediately enter the coarse-tracking of the power increment, anduse the Ppv-Vpv curve as the tracking standard. Using FIG. 1( b) as anexample to describe the MPPT of the present invention, for example, ifthe detected voltage and current, and the computed power at certainmoment respectively fall on point A of Ipv-Vpv curve, and point A′ ofthe Ppv-Vpv curve, and the computed power increment ΔP=P_(n+1)−P_(n)falls outside the range of threshold (P_(ρ1), P_(ρ2)), the system willimmediately employ the power increment tracking and use the Ppv-Vpvcurve as a tracking standard so as to drive the point A′ to be moved topoint C′ rapidly and to track until the power threshold point P_(ρ1).Correspondingly, the point A on the Ipv-Vpv curve is moved to C duringthis period and is tracked until the threshold point ρ1. The trackingfunction of the power increment principle in this area is relativelysensitive and definite than that of the conventional incrementalconductance principle. Similarly, if the detected voltage and current,and the computed power respectively fall on point B of Ipv-Vpv curve,and point B′ of the Ppv-Vpv curve, as aforementioned, the same powerincrement tracking principle will be employed to engage in the trackingphenomenon. If the detected voltage and current, and the computed powerrespectively fall in the range of threshold (P_(ρ1), P_(ρ2)), that isthe corresponding range of (ρ1, ρ2), the system will immediately startthe fine-tracking of the incremental conductance tracking, use theIpv-Vpv curve as the tracking standard, and thus the system can veryquickly reach the MPP C (i.e. ΔI/ΔV=−I/V), corresponding to the MPP C′(i.e. dP/dV=0). This technique can not only improve the slow trackingspeed of the incremental conductance method, but also ensure theaccuracy of the MPPT, and increase the efficiency of the MPPT. FIGS. 2(a)-2(b) respectively show the waveform diagrams of the various trackingroutes of the PI-INC MPPT method proposed by the present invention andthe INC MPPT method when it is fallen on the right-hand side and theleft-hand side of the MPP. As shown in FIG. 2( a), when the PI-INC MPPTmethod proposed by the present invention is used, and it is fallen onthe right-hand side of the MPP, the Ppv-Vpv curve is used to trackfirstly, and then the Ipv-Vpv curve is used when the range of (ρ1, ρ2)is entered. As shown in FIG. 2( b), when the PI-INC MPPT method proposedby the present invention is used, and it is fallen on the left-hand sideof the MPP, the Ppv-Vpv curve is used to track firstly, and then theIpv-Vpv curve is used when the range of (ρ1, ρ2) is entered. As for theINC MPPT method, it uses the Ipv-Vpv curve to track no matter where itfalls on.

According to FIG. 1( a), the typical I_(pv)-V_(pv), relationship of apractical photovoltaic cell, neglecting R_(sh), can be described by

$\begin{matrix}{\mspace{79mu} {{I_{pv} = {I_{ph} - {I_{pvo}\left\{ {{\exp \left\lbrack {\frac{q}{AkT}\left( {V_{pv} + {I_{pv}R_{s}}} \right)} \right\rbrack} - 1} \right\}}}}\mspace{20mu} {and}}} & \left( 1^{\prime} \right) \\{\mspace{79mu} {{V_{pv} = {{\frac{AkT}{q}{\ln\left( \frac{I_{ph} - I_{pv} + I_{pvo}}{I_{pvo}} \right)}} - {I_{pv}R_{s}}}}\mspace{20mu} {and}}} & (2) \\{\frac{I_{pv}}{V_{pv}} = {{- \frac{q}{AkT}}I_{pvo}{^{\frac{q}{AkT}{({V_{pv} + {I_{pv}R_{s}}})}}\left( {1 + {\frac{q}{AkT}R_{s}I_{pvo}^{\frac{q}{AkT}{({V_{pv} + {I_{pv}R_{s}}})}}}} \right)}^{- 1}}} & (3)\end{matrix}$

where I_(ph) denotes light-generated current, I_(pvo) is dark saturationcurrent, I_(pv) is PV electric current, V_(pv) is PV voltage, R_(s) isseries resistance, A is the non-ideality factor, k is Boltzmann'sconstant, T is temperature, and q is the electronic charge. The outputpower from the PV cell can be given by

$\begin{matrix}{\begin{matrix}{P_{pv} = {V_{pv}I_{pv}}} \\{= {I_{pv}\left\{ {{\frac{AkT}{q}{\ln \left( \frac{I_{ph} - I_{pv} + I_{pvo}}{I_{pvo}} \right)}} - {I_{pv}R_{s}}} \right\}}}\end{matrix}{and}} & (4) \\{\frac{P_{pv}}{V_{pv}} = {I_{pv} + {V_{pv} \cdot \frac{I_{pv}}{V_{pv}}}}} & (5)\end{matrix}$

The MPP in the PV array occurs when

$\begin{matrix}{\frac{P_{pv}}{V_{pv}} = 0} & (6)\end{matrix}$

The criteria for the INC MPPT at MPP can then be given from (6),

$\begin{matrix}{\frac{I_{pv}}{V_{pv}} = {- \frac{I_{pv}}{V_{pv}}}} & (7)\end{matrix}$

Referring to FIG. 1( b), dP_(pv)/dV_(pv)=0 on the Ppv-Vpv curve is equalto MPP of dI_(pv)/dV_(pv)=−I_(pv)/V_(pv) on the ipv-vpv curve. Indifference expression, (7) becomes

$\begin{matrix}{{\frac{\Delta \; I_{pv}}{\Delta \; V_{pv}} \approx \frac{I_{pv}}{V_{pv}}} = {- \frac{I_{pv}}{V_{pv}}}} & (8)\end{matrix}$

and (8) can also be represented by

ΔI _(pv) V _(pv) +ΔV _(pv) I _(pv)=0  (9)

From ΔC as shown via the I_(pv)-V_(pv) curve, the boundaries of theproposed INC MPPT method are,

$\begin{matrix}{{{- \rho_{1}}\frac{I_{pv}}{V_{pv}}} > {\Delta \; C} > {{- \rho_{2}}\frac{I_{pv}}{V_{pv}}}} & (10)\end{matrix}$

for INC tracking along the I_(pv)-V_(pv) curve in CTZ (or TTZ), and

$\begin{matrix}{{{\Delta \; C} > {{- \rho_{1}}\frac{I_{pv}}{V_{pv}}}}{or}} & (11) \\{{\Delta \; C} < {{- \rho_{2}}\frac{I_{pv}}{V_{pv}}}} & (12)\end{matrix}$

for the PI tracking along the P_(pv)-V_(pv) curve beyond the CTZ (orTTZ), but in the sense of INC MPPT, it is for INC tracking along theI_(pv)-V_(pv) curve, where the ΔC is defined as

$\begin{matrix}{{\Delta \; C} = \frac{\Delta \; I_{pv}}{\Delta \; V_{pv}}} & (13)\end{matrix}$

where the two ratios ρ₁ and ρ₂ are real numbers and let ρ_(m)=1 at MPP.Equation (13) is negative because the signs of ΔI_(pv) and ΔV_(pv) arealways opposite. Accordingly, from (8) and (10),

$\begin{matrix}{{- \rho_{1}} > \frac{\Delta \; I_{pv}V_{pv}}{\Delta \; V_{pv}I_{pv}} > {- \rho_{2}}} & (14)\end{matrix}$

From (5), by difference approach,

$\begin{matrix}\begin{matrix}{{P_{pv}} \approx {\Delta \; P_{pv}}} \\{= {{V_{pv}\Delta \; I_{pv}} + {I_{pv}\Delta \; V_{pv}}}}\end{matrix} & (15)\end{matrix}$

All increments in (15) are defined as follows.

ΔP=P _(n+1) −P _(n)  (16)

ΔV=V _(n+1) −V _(n)  (17)

and

ΔI=I _(n+1) −I _(n)  (18)

where all subscripts pv are omitted for simplicity in analysis, suchthat ΔP=ΔP_(pv), ΔV=ΔV_(pv), and ΔI=AΔI_(pv). Related to the definitionof the CTZ in (10), a corresponding PTZ is equivalently defined by

P _(ρ1) >ΔP>P _(ρ2)  (19)

for PI-INC MPPT in PTZ (or TTZ), which uses INC tracking toward MPPalong the I_(pv)-V_(pv) curve, and

ΔP>P _(ρ1)  (20)

or

ΔP<P _(ρ2)  (21)

for PI-INC MPPT excluding the PTZ (or TTZ), which uses the PI trackingtoward either point P_(ρ1) or P_(ρ2) along the P_(pv)-V_(pv) curve.Subsequently, by adding one to all terms in (14) yields

$\begin{matrix}{{{1 - \rho_{1}} > {\frac{\Delta \; {IV}_{n + 1}}{\Delta \; {VI}_{n + 1}} + 1} > {1 - \rho_{2}}}{and}} & (22) \\{{\left( {1 - \rho_{1}} \right)\Delta \; {VI}_{n + 1}} > {\Delta \; P} > {\left( {1 - \rho_{2}} \right)\Delta \; {VI}_{n + 1}}} & (23)\end{matrix}$

where ΔV and ΔI have opposite signs and ρ₂>ρ_(m)>ρ₁ with ρ_(m)=1. Thetwo power threshold limits in (23) are then defined by

P _(ρ1)≡(1−ρ₁)ΔVI _(n+1)  (24)

and

P _(ρ2)≡(1−ρ₂)ΔVI _(n+1)  (25)

If 1−ρ₂=−(1−ρ₁) is adopted for example, then the values of (24) and (25)are equal and yield

P _(ρ2=−P) _(ρ1)  (26)

and from (19),

P _(ρ1>ΔP>−P) _(ρ1)  (27)

A summary of the tracking of PI-INC MPPT is briefly described asfollows:

Case I: Tracking in TTZ zone: the priority measure for guiding judgmentis ΔC in (10) and the minor for monitoring is ΔP in (19).

(1) The PI-INC MPPT guides the PV converter using INC tracking along theI_(pv)-V_(pv) curve toward MPP.

(2) Once ΔC=−I_(n+1)/V_(n+1), corresponding to ΔP=0, the system willexactly operate at MPP that is kept by the PI-INC MPPT using INCtracking along the I_(pv)-V_(pv) curve.

Case II: Tracking beyond the TTZ zone: the priority measure for guidingjudgment is ΔP in (19) and the minor for monitoring is ΔC in (10).

(1) If ΔP≠0 but ΔP>P_(ρ1) in (20), in the left-hand side of TTZ, thePI-INC MPPT guides the PV converter using PI tracking along theP_(pv)-V_(pv) curve toward point P_(ρ1).

(2) If ΔP≠0 but ΔP<P_(ρ2) in (21), in the right-hand side of TTZ, thePI-INC MPPT guides the PV converter using PI tracking along theP_(pv)-V_(pv) curve toward point P_(ρ2).

As shown in FIG. 3( a), it depicts a photovoltaic system according tothe preferred embodiment of the present invention, being a charger andincluding a PI-INC MPPT controller (not shown, and only its outputsignal being indicated as a PWM with VFCD guided by the PI-INC MPPTcontroller), and the controller uses a variable-frequency constant-duty(VFCD) control, and is guided by a control chart, wherein the controlchart includes an Ipv-Vpv curve and a Ppv-Vpv curve, a dIpv/dVpv-Vpvcurve, a dIpv/dVpv-fs curve, and a Po-fs curve (the above-mentionedcurves are shown in FIG. 4). Besides, the photovoltaic system furtherincludes a PV array, an interleaved flyback converter, a battery, diodesD1 and DT1, capacitor CB and inverter A2. The interleaved flybackconverter is electrically connected to the PV array, and the battery iselectrically connected to the interleaved flyback converter. Theinterleaved flyback converter includes a first flyback converter(flyback(1), having switch QF1, transformer T1 and diode DFs1) and asecond flyback converter (flyback(2), having switch QF2, transformer T2and diode DFs2), the first flyback converter is electrically connectedto the second flyback converter in parallel, and the first and thesecond flyback converters receive a pulse-width modulation signal (i.e.the PWM with VFCD) from the PI-INC controller so as to cause the systemto engage in an MPPT.

In FIG. 3( a), the inner resistance r_(Lm) of the transformer isneglected and all parameters of the two flyback converters are presumedthe same to facilitate analysis. The predicted dynamic-state waveformsof the IFC are shown in FIG. 3( b), in which the primary currents,i_(p1) and i_(p2), that are interleaved pumping from the PV array, andthe secondary currents, i_(s1) and i_(s2), that are to be synthesized atnode M as i_(s)=i_(o,if)=i_(B) for charging the battery (it is alead-acid battery (LAB)). To suit the interleaved operation, both twoflyback converters are designed to operate betweendiscontinuous-continuous conduction mode (DCM) and boundary conductionmode (BCM) so that the pulse charge can prevent the sulfatingcrystallization from covering the positive electrode of LAB, prolongingthe battery life. However, only the IFC in BCM is analyzed forconvenience. An equivalent half-circuit of the IFC is shown in FIG. 3(c). In FIG. 3( a), the peak primary current î_(p1)=î_(pv1) of theflyback converter (I) from the PV array can be given by

$\begin{matrix}{{\hat{i}}_{{pv}\; 1} = {\frac{V_{pv}}{L_{m}}t_{on}}} & (28)\end{matrix}$

The average primary current I_(pv1) in each drawing period T_(s) isequal to that I_(pv2) for flyback converter (II),

$\begin{matrix}\begin{matrix}{I_{{pv}\; 1} = \frac{V_{pv}d^{2}}{2L_{m}f_{s}}} \\{= I_{{pv}\; 2}}\end{matrix} & (29)\end{matrix}$

where d is duty cycle, L_(m) is magnetizing inductance, and f_(s) isswitching frequency (or control frequency). For convenience in analysisand synthesis of the pulse train for charger, the instantaneous primarycurrents i_(p1) and i_(p2) of IFC from PV array are then defined as

$\begin{matrix}{i_{p\; 1} = \left\{ {\begin{matrix}\frac{V_{pv}}{L_{m}} & {0 < t < {dT}_{s}} \\0 & {{dT}_{s} < t < T_{s}}\end{matrix}{And}} \right.} & (30) \\{i_{p\; 2} = \left\{ \begin{matrix}{\frac{V_{pv}}{L_{m}}\left( {t - \frac{T_{s}}{2}} \right)} & {\frac{T_{s}}{2} < t < \left( {\frac{T_{s}}{2} + {dT}_{s}} \right)} \\0 & {Otherwise}\end{matrix} \right.} & (31)\end{matrix}$

We then have total average PV current I_(pv) that is drawn by IFC, from(29),

$\begin{matrix}{I_{pv} = \frac{V_{pv}d^{2}}{L_{m}f_{s}}} & (32)\end{matrix}$

If power efficiency η is considered, the relation of output power P_(o)and input power P_(pv) with a load of battery V_(B) can be expressed as

ηI _(pv) V _(pv) =I _(o,if) V _(B) =I _(s) V _(B)  (33)

Where V_(o)=V_(B), P_(o)=I_(o,if)V_(B)=I_(s)V_(B) andP_(pv)=I_(pv)V_(pv).

From (29), the two average secondary (output) currents before synthesiscan then be given by

$\begin{matrix}\begin{matrix}{I_{s\; 1} = I_{s\; 2}} \\{= \frac{{\eta \left( {V_{pv}d} \right)}^{2}}{2V_{B}L_{m}f_{s}}}\end{matrix} & (34)\end{matrix}$

After the synthesis of I_(s1) and I_(s2) at node M, the output currentI_(o, if)=I_(s)=I_(B) can be expressed as

$\begin{matrix}\begin{matrix}{I_{o,{if}} = I_{s}} \\{= {I_{s\; 1} + I_{s\; 2}}} \\{= I_{B}} \\{= \frac{{\eta \left( {V_{pv}d} \right)}^{2}}{V_{B}L_{m}f_{s}}}\end{matrix} & (35)\end{matrix}$

and the output power versus switching frequency will be

$\begin{matrix}\begin{matrix}{P_{o,{if}} = {I_{B}V_{B}}} \\{= \frac{{\eta \left( {V_{pv}d} \right)}^{2}}{L_{m}f_{s}}}\end{matrix} & (36)\end{matrix}$

Formula (36) is put into the control chart as shown in FIG. 4 to be adesign reference. From (33), we then have control-to-output transferfunction of IFC given by

$\begin{matrix}{\frac{I_{o,{if}}}{f_{s}^{- 1}} = \frac{{\eta \left( {V_{pv}d} \right)}^{2}}{V_{B}L_{m}}} & (37)\end{matrix}$

In summary, the input impedance Z_(IF) of IFC should be conjugated tothe impedance Z_(pv) of the PV array for maximum power transfer, thatis,

$\begin{matrix}{{Z_{IF} = {\overset{\_}{Z}}_{pv}}{where}} & (38) \\{{Z_{IF} = {j\; 2\pi \; f_{s}L_{m}}}{And}} & (39) \\{Z_{pv} = \frac{1}{j\; 2\pi \; f_{s}C_{pv}}} & (40)\end{matrix}$

It is feasible for the PI-INC MPPT to guide the IFC drawing energy fromthe PV array under impedance matching with (38) and (39). If theinternal resistances between the PV array and the IFC are neglected forconvenience, we then have the design reference, at maximum powertransfer,

$\begin{matrix}{{L_{m}C_{pv}} = \left( \frac{1}{2\pi \; f_{s}} \right)^{2}} & (41)\end{matrix}$

An algorithm of PI-INC MPPT using VFCD is depicted in FIGS. 5( a)-(b).The algorithm is programmed according to the derived formulas (10) and(19), and refers to the control chart as shown in FIG. 4. The outlinesof the algorithm are listed in FIGS. 5( a)-(b). In FIG. 5( a), the mainprogram samples the instantaneous information come from the PV array asthe new data to be used in the subroutine of FIG. 5( b). The subroutineuses the data from the main program to calculate the instantaneous PVvoltage, current and power firstly, and then uses the standards informulas (10) and (19) to execute the PI-INC MPPT. The main programprovides a direction Dn at the very beginning, it is 1 or 0, to changethe frequency so as to decrease or increase the PV current respectively.Thus, at the very beginning, a PI fine adjustment or an INC coarseadjustment towards the MPP is engaged in. In this algorithm, a powerdifference comparison is accomplished by referring to formula (19) andcompared with Pρ1 of formula (24) and Pρ2 of formula (25). In otherwords, via the two power inequalities (20) and (21), the direction oftracking is quite easy to be determined.

DESIGN AND EXPERIMENT

The algorithm of PI-INC MPPT is executed by Microchip dsPIC33FJ06GS202according to the guided flowchart in FIGS. 5( a)-(b). Besides, anexperimental setup with two PV arrays in series with a maximum power of250 W, and one LAB has a specification of 45 AH, is established with thecircuit structure as shown in FIG. 3( a). The charger is specified tocharge with a positive peak current pulse of 24 A for IFC to battery.The interleaved frequency f_(s) of the IFCs for drawing energy with aduty ratio of 0.26 from the PV array is set to 14.6 kHz (which is thefrequency at the MPP under solar insolation of 1 kW/m²). FIGS. 6( a)-(b)respectively show the reactions of IFC using the VFCD control, whereinFIG. 6( a) shows the waveform of output current versus switchingfrequency, and FIG. 6( b) shows the waveform of output power versusswitching frequency, in which the solid line shows the results of thesimulation, and the dotted line shows the results of the experiment(including three solar insolation, 300 W/m², 600 W/m², and 1 kW/m²). InFIGS. 6( a)-(b), the results of simulation are quite close to theresults of the experimental measurement. Thus, the tracking chart (seeFIG. 4) of PI-INC MPPT is useful in guiding practical design.

FIGS. 7( a)-(b) respectively show the interleaved high frequency tinypulse currents (ip1, ip2) and the interleaved secondary side currents(is1, is2) under the sun insolation of 1 Kw/m². All the peak valuescurrents are approximately 24 A, wherein the measured waveforms are thesame as those predicted by FIG. 3( b).

FIG. 8 compares PI-INC MPPT and INC-MPPT in terms of dynamic trackingbehavior for various insolation changes, in which the tracking timeresponses to MPP are estimated for five kinds of scenarios of insolationchange. This comparison reveals that PI-INC MPPT has a faster trackingperformance than that of INC MPPT over 3-4 times during a large changein insolation.

Embodiments

1. A photovoltaic system with a photovoltaic current (Ipv), aphotovoltaic voltage (Vpv), a photovoltaic power (Ppv), a controlfrequency (fs) and an output power (Po), wherein there is a derivative(dIpv/dVpv) of Ipv with respect to Vpv, comprising:

a power-increment-aided incremental-conductance (PI-INC) maximum powerpoint tracking (MPPT) controller guided by a control chart, wherein thecontrol chart includes:

an Ipv-Vpv curve and a Ppv-Vpv curve;

a dIpv/dVpv-Vpv curve;

a dIpv/dVpv-fs curve; and

a Po-fs curve.

2. A system according to Embodiment 1, wherein the PI-INC MPPTcontroller uses a variable frequency constant duty control.

3. A system according to Embodiment 2 or 3, wherein the system is oneselected from a group consisting of a photovoltaic charger, aphotovoltaic DC link converter and a photovoltaic inverter.

4. A system according to anyone of the above-mentioned Embodiments beingthe photovoltaic charger and further comprising a photovoltaic (PV)array, an interleaved flyback converter and a battery, wherein theinterleaved flyback converter is electrically connected to the PV array,the battery is electrically connected to the interleaved flybackconverter, the interleaved flyback converter includes a first flybackconverter and a second flyback converter, the first flyback converter iselectrically connected to the second flyback converter in parallel, andthe first and the second flyback converters receive a pulse-widthmodulation signal from the PI-INC MPPT controller to cause the system toperform an MPPT.

5. A system according to anyone of the above-mentioned embodiments,wherein when a specific conductance derivative ratio on the Ipv-Vpvcurve is located in a threshold tracking zone having a minimum valuelarger than a first conductance derivative ratio, and a maximum valuesmaller than a second conductance derivative ratio, the controller usesthe Ipv-Vpv curve to perform an INC fine tracking, when the specificconductance derivative ratio is located outside the threshold trackingzone, the controller uses the Ppv-Vpv curve to perform an PI coarsetracking, and when the first conductance derivative ratio is ρ1 and thesecond conductance derivative ratio is ρ2,

${{- \rho_{1}} > \frac{\Delta \; I_{pv}V_{pv}}{\Delta \; V_{pv}I_{pv}} > {- \rho_{2}}},$

where Vpv is an output voltage of the PV array, Ipv is an output currentof the PV array, ΔIpv is a change of the Ipv, and ΔVpv is a change ofthe Vpv.

6. A photovoltaic system with a photovoltaic current (Ipv), aphotovoltaic voltage (Vpv) and a photovoltaic power (Ppv), comprising:

a controller having circuit characteristics represented by an Ipv-Vpvcurve and a Ppv-Vpv curve.

7. A photovoltaic system according to Embodiment 6 further comprising acontrol frequency (fs) and an output power (Po), wherein there is aderivative (dIpv/dVpv) of Ipv with respect to Vpv, the circuitcharacteristics are further represented by a dIpv/dVpv-Vpv curve, adIpv/dVpv-fs curve, and a Po-fs curve.

8. A photovoltaic system according to Embodiment 6 or 7, wherein thecontroller is guided by the circuit characteristics such that thephotovoltaic system is engaged in an MPPT.

9. A system according to anyone of the above-mentioned Embodiment,wherein the system is one selected from a group consisting of aphotovoltaic charger, a photovoltaic DC link converter and aphotovoltaic inverter.

10. A system according to anyone of the above-mentioned embodimentsbeing the photovoltaic charger and further comprising a photovoltaic(PV) array, an interleaved flyback converter and a battery, theinterleaved flyback converter is electrically connected to the PV array,the battery is electrically connected to the interleaved flybackconverter, the interleaved flyback converter includes a first flybackconverter and a second flyback converter, the first flyback converter iselectrically connected to the second flyback converter in parallel, andthe first and the second flyback converters receive a pulse-widthmodulation signal from the PI-INC MPPT controller to cause the system toengage in an MPPT.

11. A system according to anyone of the above-mentioned embodiments,wherein when a specific conductance derivative ratio on the Ipv-Vpvcurve is located in a threshold tracking zone having a minimum valuelarger than a first conductance derivative ratio, and a maximum valuesmaller than a second conductance derivative ratio, the controller usesthe Ipv-Vpv curve to engage in an INC fine tracking, when the specificconductance derivative ratio is located outside the threshold trackingzone, the controller uses the Ppv-Vpv curve to engage in a PI coarsetracking, and when the first conductance derivative ratio is ρ1 and thesecond conductance derivative ratio is ρ2,

${{- \rho_{1}} > \frac{\Delta \; I_{pv}V_{pv}}{\Delta \; V_{pv}I_{pv}} > {- \rho_{2}}},$

where Vpv is an output voltage of the PV array, Ipv is an output currentof the PV array, ΔIpv is a change of the Ipv, and ΔVpv is a change ofthe Vpv.

12. A method for operating a controller of a photovoltaic system with aphotovoltaic current (Ipv), a photovoltaic voltage (Vpv) and aphotovoltaic power (Ppv), comprising a step of: providing a Ipv-Vpvcurve and a Ppv-Vpv curve to be used to determine whether a specificconductance derivative ratio of dIpv/dVpv enters a threshold trackingzone.

13. A method according to anyone of the above-mentioned embodiments,wherein the threshold tracking zone having a minimum value larger than afirst conductance derivative ratio, and a maximum value smaller than asecond conductance derivative ratio, the Ipv-Vpv curve, the Ppv-Vpvcurve and the threshold tracking zone are provided to guide thecontroller, the method further comprising a step of: a) causing thecontroller to use a variable-frequency constant-duty control to engagein an MPPT.

14. A method according to Embodiment 12 or 13 further comprising a stepof: b) causing the controller to use the Ipv-Vpv curve to engage in anINC fine tracking when the specific conductance derivative ratio on theIpv-Vpv curve is located in the threshold tracking zone.

15. A method according to anyone of the above-mentioned Embodimentsfurther comprising a step of: c) causing the controller to use thePpv-Vpv curve to engage in a PI coarse tracking when the specificconductance derivative ratio is located outside the threshold trackingzone.

16. A method according to Embodiment 14 or 15, wherein the photovoltaicsystem further comprises a photovoltaic (PV) array, and when the firstconductance derivative ratio is ρ1 and the second conductance derivativeratio is ρ2,

${{- \rho_{1}} > \frac{\Delta \; I_{pv}V_{pv}}{\Delta \; V_{pv}I_{pv}} > {- \rho_{2}}},$

where Vpv is an output voltage of the PV array, Ipv is an output currentof the PV array, ΔIpv is a change of the output current of the PV arrayIpv, and ΔVpv is a change of the output voltage Vpv of the PV array.

17. A method according to anyone of the above-mentioned embodiments,wherein the step b) further comprises sub-steps of:

when the specific conductance derivative ratio is smaller than β1,causing the Vpv to increase a positive value of ΔVpv via the controllerso as to get a change ΔPpv of an output power Ppv of the PV array viathe Ppv-Vpv curve and to stop when ΔPpv/ΔVpv≈dPpv/dVpv=0, wheredPpv/dVpv is a derivative of Ppv with respect to Vpv;

when the specific conductance derivative ratio is larger than ρ2,causing the Vpv to decrease the positive value of ΔVpv via thecontroller so as to get the change ΔPpv of the output power Ppv of thePV array via the Ppv-Vpv curve and to stop when ΔPpv/ΔVpv≈dPpv/dVpv=0;

when ρ1≦the conductance derivative ratio≦ρ2 and ΔIpv/ΔVpv>−Ipv/Vpv,causing the Vpv to increase the positive value of ΔVpv via thecontroller so as to get a change ΔIpv of the output current Ipv of thePV array via the Ipv-Vpv curve and to stop when ΔIpv/ΔVpv=−Ipv/Vpv; and

when ρ1≦the conductance derivative ratio≦ρ2 and ΔIpv/ΔVpv<−Ipv/Vpv,causing the Vpv to decrease the positive value of ΔVpv via thecontroller so as to get the change ΔIpv of the output current Ipv of thePV array via the Ipv-Vpv curve and to stop when ΔIpv/ΔVpv=−Ipv/Vpv.

According to the aforementioned descriptions, the present inventionprovides a photovoltaic system having a power-increment-aidedincremental-conductance maximum power point tracking controller using avariable-frequency constant-duty control. This technique includesPI-MPPT and INC-MPPT, and sets up a threshold tracking zone in the areawith obvious changes on the Ipv-Vpv curve around point C. If the powerincrement falls into the threshold tracking zone, the system enters theINC fine tracking and uses the Ipv-Vpv curve as a tracking standard. Onthe contrary, if the power increment falls outside the thresholdtracking zone, the system enters the PI coarse tracking and uses thePpv-Vpv curve as a tracking standard. The proposed photovoltaic systemhas a relatively quick response and a relatively better outputefficiency of the maximum power when engaged in the MPPT so as topossess the non-obviousness and the novelty.

While the present invention has been described in terms of what arepresently considered to be the most practical and preferred embodiments,it is to be understood that the present invention need not be restrictedto the disclosed embodiments. On the contrary, it is intended to covervarious modifications and similar arrangements included within thespirit and scope of the appended claims which are to be accorded withthe broadest interpretation so as to encompass all such modificationsand similar structures. Therefore, the above description andillustration should not be taken as limiting the scope of the presentinvention which is defined by the appended claims.

What is claimed is:
 1. A photovoltaic system with a photovoltaic current(Ipv), a photovoltaic voltage (Vpv), a photovoltaic power (Ppv), acontrol frequency (fs) and an output power (Po), wherein there is aderivative (dIpv/dVpv) of Ipv with respect to Vpv, comprising: apower-increment-aided incremental-conductance (PI-INC) maximum powerpoint tracking (MPPT) controller guided by a control chart, wherein thecontrol chart includes: an Ipv-Vpv curve and a Ppv-Vpv curve; adIpv/dVpv-Vpv curve; a dIpv/dVpv-fs curve; and a Po-fs curve.
 2. Asystem according to claim 1, wherein the PI-INC MPPT controller uses avariable frequency constant duty control.
 3. A system according to claim1, wherein the system is one selected from a group consisting of aphotovoltaic charger, a photovoltaic DC link converter and aphotovoltaic inverter.
 4. A system according to claim 3 being thephotovoltaic charger and further comprising a photovoltaic (PV) array,an interleaved flyback converter and a battery, wherein the interleavedflyback converter is electrically connected to the PV array, the batteryis electrically connected to the interleaved flyback converter, theinterleaved flyback converter includes a first flyback converter and asecond flyback converter, the first flyback converter is electricallyconnected to the second flyback converter in parallel, and the first andthe second flyback converters receive a pulse-width modulation signalfrom the PI-INC MPPT controller to cause the system to perform an MPPT.5. A system according to claim 4, wherein when a specific conductancederivative ratio on the Ipv-Vpv curve is located in a threshold trackingzone having a minimum value larger than a first conductance derivativeratio, and a maximum value smaller than a second conductance derivativeratio, the controller uses the Ipv-Vpv curve to perform an INC finetracking, when the specific conductance derivative ratio is locatedoutside the threshold tracking zone, the controller uses the Ppv-Vpvcurve to perform an PI coarse tracking, and when the first conductancederivative ratio is ρ1 and the second conductance derivative ratio isρ2,${{- \rho_{1}} > \frac{\Delta \; I_{pv}V_{pv}}{\Delta \; V_{pv}I_{pv}} > {- \rho_{2}}},$where Vpv is an output voltage of the PV array, Ipv is an output currentof the PV array, ΔIpv is a change of the Ipv, and ΔVpv is a change ofthe Vpv.
 6. A photovoltaic system with a photovoltaic current (Ipv), aphotovoltaic voltage (Vpv) and a photovoltaic power (Ppv), comprising: acontroller having circuit characteristics represented by an Ipv-Vpvcurve and a Ppv-Vpv curve.
 7. A system according to claim 6 furthercomprising a control frequency (fs) and an output power (Po), whereinthere is a derivative (dIpv/dVpv) of Ipv with respect to Vpv, thecircuit characteristics are further represented by a dIpv/dVpv-Vpvcurve, a dIpv/dVpv-fs curve, and a Po-fs curve.
 8. A system according toclaim 7, wherein the controller is guided by the circuit characteristicssuch that the photovoltaic system is engaged in an MPPT.
 9. A systemaccording to claim 7, wherein the system is one selected from a groupconsisting of a photovoltaic charger, a photovoltaic DC link converterand a photovoltaic inverter.
 10. A system according to claim 9 being thephotovoltaic charger and further comprising a photovoltaic (PV) array,an interleaved flyback converter and a battery, the interleaved flybackconverter is electrically connected to the PV array, the battery iselectrically connected to the interleaved flyback converter, theinterleaved flyback converter includes a first flyback converter and asecond flyback converter, the first flyback converter is electricallyconnected to the second flyback converter in parallel, and the first andthe second flyback converters receive a pulse-width modulation signalfrom the PI-INC MPPT controller to cause the system to engage in anMPPT.
 11. A system according to claim 10, wherein when a specificconductance derivative ratio on the Ipv-Vpv curve is located in athreshold tracking zone having a minimum value larger than a firstconductance derivative ratio, and a maximum value smaller than a secondconductance derivative ratio, the controller uses the Ipv-Vpv curve toengage in an INC fine tracking, when the specific conductance derivativeratio is located outside the threshold tracking zone, the controlleruses the Ppv-Vpv curve to engage in a PI coarse tracking, and when thefirst conductance derivative ratio is ρ1 and the second conductancederivative ratio is ρ2,${{- \rho_{1}} > \frac{\Delta \; I_{pv}V_{pv}}{\Delta \; V_{pv}I_{pv}} > {- \rho_{2}}},$where Vpv is an output voltage of the PV array, Ipv is an output currentof the PV array, ΔIpv is a change of the Ipv, and ΔVpv is a change ofthe Vpv.
 12. A method for operating a controller of a photovoltaicsystem with a photovoltaic current (Ipv), a photovoltaic voltage (Vpv)and a photovoltaic power (Ppv), comprising a step of: providing anIpv-Vpv curve and a Ppv-Vpv curve to be used to determine whether aspecific conductance derivative ratio of dIpv/dVpv enters a thresholdtracking zone.
 13. A method according to claims 12, wherein thethreshold tracking zone having a minimum value larger than a firstconductance derivative ratio, and a maximum value smaller than a secondconductance derivative ratio, the Ipv-Vpv curve, the Ppv-Vpv curve andthe threshold tracking zone are provided to guide the controller, themethod further comprising a step of: a) causing the controller to use avariable-frequency constant-duty control to engage in an MPPT.
 14. Amethod according to claims 13 further comprising a step of: b) causingthe controller to use the Ipv-Vpv curve to engage in an INC finetracking when the specific conductance derivative ratio on the Ipv-Vpvcurve is located in the threshold tracking zone.
 15. A method accordingto claims 14 further comprising a step of: c) causing the controller touse the Ppv-Vpv curve to engage in a PI coarse tracking when thespecific conductance derivative ratio is located outside the thresholdtracking zone.
 16. A method according to claim 13, wherein thephotovoltaic system further comprises a photovoltaic (PV) array, andwhen the first conductance derivative ratio is ρ1 and the secondconductance derivative ratio is ρ2,${{- \rho_{1}} > \frac{\Delta \; I_{pv}V_{pv}}{\Delta \; V_{pv}I_{pv}} > {- \rho_{2}}},$where Vpv is an output voltage of the PV array, Ipv is an output currentof the PV array, ΔIpv is a change of the output current of the PV arrayIpv, and ΔVpv is a change of the output voltage Vpv of the PV array. 17.A method according to claim 16, wherein the step b) further comprisessub-steps of: when the specific conductance derivative ratio is smallerthan ρ1, causing the Vpv to increase a positive value of ΔVpv via thecontroller so as to get a change ΔPpv of an output power Ppv of the PVarray via the Ppv-Vpv curve and to stop when ΔPpv/ΔVpv≈dPpv/dVpv=0,where dPpv/dVpv is a derivative of Ppv with respect to Vpv; when thespecific conductance derivative ratio is larger than ρ2, causing the Vpvto decrease the positive value of ΔVpv via the controller so as to getthe change ΔPpv of the output power Ppv of the PV array via the Ppv-Vpvcurve and to stop when ΔPpv/ΔVpv≈dPpv/dVpv=0; when ρ1≦the conductancederivative ratio≦ρ2 and ΔIpv/ΔVpv>−Ipv/Vpv, causing the Vpv to increasethe positive value of ΔVpv via the controller so as to get a change ΔIpvof the output current Ipv of the PV array via the Ipv-Vpv curve and tostop when ΔIpv/ΔVpv=−Ipv/Vpv; and when ρ1≦the conductance derivativeratio≦ρ2 and ΔIpv/ΔVpv<−Ipv/Vpv, causing the Vpv to decrease thepositive value of ΔVpv via the controller so as to get the change ΔIpvof the output current Ipv of the PV array via the Ipv-Vpv curve and tostop when ΔIpv/ΔVpv=−Ipv/Vpv.